The following four waves are sent along strings with the same
linear densities (x is in meters and t is in seconds). Rank the waves according to (a) their wave speed and (b) the tension in the strings along which they travel, greatest first:
1 $y_1 = (3 mm) sin(x - 3t)$, (1) $y_2 = (6 mm) sin(2x - t)$, (3) $y_3 = (1 mm) sin(4x - t)$, (4) $y_4 = (2 mm) sin(x - 2t)$,

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Xema8 Xema8 · Answer 1 · 2020-06-23T06:43:59+02:00

Answer:

Explanation:

y_1 = (3 mm) sin(x - 3t)

comparing it with standard wave equation

y = A sin( ωt-kx )

we see

ω = -3 , k = -1

velocity = ω / k

= 3

y_2 = (6 mm) sin(2x - t)

we see

ω = -1 , k = -2

velocity = ω / k

= .5

y_3 = (1 mm) sin(4x - t)

we see

ω = -1 , k = -4

velocity = ω / k

= .25

y_4 = (2 mm) sin(x - 2t)

we see

ω = -2 , k = -1

velocity = ω / k

= 2

So greatest velocity to lowest velocity

y_1 = (3 mm) sin(x - 3t) , y_4 = (2 mm) sin(x - 2t) ,y_2 = (6 mm) sin(2x - t) , y_3 = (1 mm) sin(4x - t)

b )

Given the mass per unit length of wire the same , velocity is proportional to

√ T , where T is tension

so in respect of tension in the wire same order will exist for highest to lowest tension .